Jones, who tops the junior girls' world rankings, pushed world No.9 Kasatkina all the way in their Adelaide International meeting on Wednesday night.
The 16-year-old from the Gold Coast won the first two games of the opening set without dropping a point, but was eventually beaten 7-5 6-3 by her vastly more experienced opponent.
Kasatkina, a French Open semi-finalist and Wimbledon quarter-finalist, was troubled at times by Jones' clean and powerful ground strokes.
"It was a pretty intense match," Kasatkina said after the match.
"I'm really happy with how I was able to come back after a very quick beginning, let's say, of the match.
"She's got really good tennis, so I'm already a bit scared, to be honest. She's just 16 (years old)."
Jones has already drawn comparisons with three-time major champion Ash Barty and won plenty of admirers this week in Adelaide.
She banked her first win over a WTA top-50 ranked player, sweeping aside China's world No.37 Wang Xinyu 6-4 6-0 in the opening round.
Kasatkina's push for a ninth career WTA title continues against American world No.20 Madison Keys in a Thursday evening quarter-final.
The 27-year-old has twice reached the final in Adelaide, losing to Jelena Ostapenko last year and Belinda Bencic the previous summer.
Sixth seed Diana Shnaider meets Yulina Putinseva in a night match, with the winner to join top seed Jessica Pegula and Liudmila Samsonova in the semi-finals.
American Pegula led compatriot Ashlyn Krueger 6-4 2-0 when her opponent retired because of an as yet undisclosed injury.
World No.26 Samsonova upset American second seed Emma Navarro 6-4 6-4.
21°C